Generalized boost transformations in finite volumes and application to Hamiltonian methods
Abstract The investigation of hadron interactions within lattice QCD has been facilitated by the well-known quantisation condition, linking scattering phase shifts to finite-volume energies. Additionally, the ability to utilise systems at finite total boosts has been pivotal in smoothly charting the...
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| Format: | Article |
| Language: | English |
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SpringerOpen
2024-08-01
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| Series: | Journal of High Energy Physics |
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| Online Access: | https://doi.org/10.1007/JHEP08(2024)178 |
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| author | Yan Li Jia-Jun Wu T.-S. H. Lee R. D. Young |
| author_facet | Yan Li Jia-Jun Wu T.-S. H. Lee R. D. Young |
| author_sort | Yan Li |
| collection | DOAJ |
| description | Abstract The investigation of hadron interactions within lattice QCD has been facilitated by the well-known quantisation condition, linking scattering phase shifts to finite-volume energies. Additionally, the ability to utilise systems at finite total boosts has been pivotal in smoothly charting the energy-dependent behaviour of these phase shifts. The existing implementations of the quantization condition at finite boosts rely on momentum transformations between rest and moving frames, defined directly in terms of the energy eigenvalues. This energy dependence is unsuitable in the formulation of a Hamiltonian. In this work, we introduce a novel approach to generalise the three-momentum boost prescription, enabling the incorporation of energy-independent finite-volume Hamiltonians within moving frames. We demonstrate the application of our method through numerical comparisons, employing a phenomenological ππ scattering example. |
| format | Article |
| id | doaj-art-d834cc70827f40dd95c981b0d3615c32 |
| institution | Kabale University |
| issn | 1029-8479 |
| language | English |
| publishDate | 2024-08-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Journal of High Energy Physics |
| spelling | doaj-art-d834cc70827f40dd95c981b0d3615c322024-11-24T12:07:42ZengSpringerOpenJournal of High Energy Physics1029-84792024-08-012024813110.1007/JHEP08(2024)178Generalized boost transformations in finite volumes and application to Hamiltonian methodsYan Li0Jia-Jun Wu1T.-S. H. Lee2R. D. Young3University of Chinese Academy of Sciences (UCAS)University of Chinese Academy of Sciences (UCAS)Physics Division, Argonne National LaboratorySpecial Research Center for the Subatomic Structure of Matter (CSSM), Department of Physics, The University of AdelaideAbstract The investigation of hadron interactions within lattice QCD has been facilitated by the well-known quantisation condition, linking scattering phase shifts to finite-volume energies. Additionally, the ability to utilise systems at finite total boosts has been pivotal in smoothly charting the energy-dependent behaviour of these phase shifts. The existing implementations of the quantization condition at finite boosts rely on momentum transformations between rest and moving frames, defined directly in terms of the energy eigenvalues. This energy dependence is unsuitable in the formulation of a Hamiltonian. In this work, we introduce a novel approach to generalise the three-momentum boost prescription, enabling the incorporation of energy-independent finite-volume Hamiltonians within moving frames. We demonstrate the application of our method through numerical comparisons, employing a phenomenological ππ scattering example.https://doi.org/10.1007/JHEP08(2024)178Algorithms and Theoretical DevelopmentsHadronic SpectroscopyStructure and Interactions |
| spellingShingle | Yan Li Jia-Jun Wu T.-S. H. Lee R. D. Young Generalized boost transformations in finite volumes and application to Hamiltonian methods Journal of High Energy Physics Algorithms and Theoretical Developments Hadronic Spectroscopy Structure and Interactions |
| title | Generalized boost transformations in finite volumes and application to Hamiltonian methods |
| title_full | Generalized boost transformations in finite volumes and application to Hamiltonian methods |
| title_fullStr | Generalized boost transformations in finite volumes and application to Hamiltonian methods |
| title_full_unstemmed | Generalized boost transformations in finite volumes and application to Hamiltonian methods |
| title_short | Generalized boost transformations in finite volumes and application to Hamiltonian methods |
| title_sort | generalized boost transformations in finite volumes and application to hamiltonian methods |
| topic | Algorithms and Theoretical Developments Hadronic Spectroscopy Structure and Interactions |
| url | https://doi.org/10.1007/JHEP08(2024)178 |
| work_keys_str_mv | AT yanli generalizedboosttransformationsinfinitevolumesandapplicationtohamiltonianmethods AT jiajunwu generalizedboosttransformationsinfinitevolumesandapplicationtohamiltonianmethods AT tshlee generalizedboosttransformationsinfinitevolumesandapplicationtohamiltonianmethods AT rdyoung generalizedboosttransformationsinfinitevolumesandapplicationtohamiltonianmethods |